let frequency be Element of REAL_Music; :: according to MUSIC_S1:def 46 :: thesis: ex o being Element of REAL_Music st [frequency,o] in octave REAL_Music
consider fr, qr being positive Real such that
A1: fr = frequency and
qr = 2 * fr and
A2: [fr,qr] in octave REAL_Music by Th41;
( fr is Element of REAL_Music & qr is Element of REAL_Music ) by Th1;
hence ex o being Element of REAL_Music st [frequency,o] in octave REAL_Music by A1, A2; :: thesis: verum